I use mostly manual primes with manual aperture rings so it's a non-issue for me, but I do have a couple without aperture rings and don't find it a problem at all. I don't ever change aperture while filming really.
D5300
Pros:
Lovely Nikon colour science
Low light performance very good
Super 35 size sensor
Dynamic range very good when using flat profile
Almost no aliasing or moire
Superb stills
Cons:
Detail is OK but not great (better than 600D, worse than G6)
Doesn't have many video features making it rather awkward to use compared to G6
G6
Pros:
Loads of detail
A pleasure to shoot with (peaking, nice EVF, good ergonomics)
Nice rich colours in well-lit situations
Cons:
Dynamic range is low (shadows can be lifted a little)
Doesn't do well in poor light - colours suffer in any situation other than bright light imo.
If you're not bothered about sound I'd look at a GX7. Colours, low light and DR are better than the G6 as far as I can see.